Description:
We discuss the determination of the longitudinal parameters of a bunched beam of electrons or positrons circulating in a storage ring. From the analysis of the beam current observed at a fixed azimuthal location, one can learn much about the longitudinal behavior. We present an elementary analysis of the time-dependence of the current. In particular, we discuss the determination of the average current, bunch length, synchrotron oscillation frequency, and the coherent synchrotron oscillation modes associated with longitudinal instabilities. A brief discussion is also given of the incoherent synchrotron oscillations, or Schottky noise. We review the electromagnetic field traveling with a charge in uniform motion, and introduce some of the most common devices used to detect this field: capacitive pick-up, stripline monitor, and DC beam current transformer. Our paper is organized as follows: We discuss the analysis of the time-dependence of the beam current. Then, the measurement of the current is considered. Finally, we describe some measurements of energy spread and bunch lengthening made recently at SLAC on the SLC damping ring. 12 refs., 6 figs.

Description:
The development of synchrotron radiation sources is discussed, emphasizing characteristics important for x-ray microscopy. Bending magnets, wigglers and undulators are considered as sources of radiation. Operating experience at the national Synchrotron Light Source on the VUV and XRAY storage rings is reviewed, with particular consideration given to achieved current and lifetime, transverse bunch dimensions, and orbit stability. 6 refs., 3 figs.

Description:
Self-sustained synchrotron oscillations are observed in electron storage rings. In general the theoretical description of the saturation of an instability for large oscillation amplitude is a difficult problem, and techniques have not yet been developed which yield analytic approximations to the appropriate nonlinear Vlasov or Fokker-Planck equations. In this paper, a single point bunch interacting with the wake field from a single resonant mode of an rf cavity is considered, and the averaging method of Bogoliubov and Mitropolsky is used to study the saturation of the initial exponential growth of the oscillation amplitude, due to the nonlinearity of the wake field. The determination of the limiting amplitude of oscillation is discussed both in the presence and in the absence of radiation damping.

Description:
The heat transfer problem associated with the incidence of synchrotron radiation upon a vacuum chamber wall cooled by a single water channel was previously studied, and a numerical solution to the potential problem was found using the two-dimensional magnet program POISSON. Calculations were extended to consider the case of a split water channel using POISSON to solve the potential problem for a given choice of parameters. By optimizing the dimensions, boiling of the water can be avoided. A copper chamber is a viable solution to the heat transfer problem at a beam port.

Description:
At the present time the first generation of facilities having electron storage rings designed for and dedicated to synchrotron radiation research are beginning operations in the US, Europe and Japan. The use of wigglers and undulators as enhanced sources of synchrotron radiation plays an important role at all these facilities. Moreover, recently there has been much activity in the design of the next generation machines, which will place even greater, and perhaps exclusive, emphasis on the use of wigglers and undulators. The operation of these insertion devices has been made even more attractive by advances in the design and construction of permanent magnet wigglers and undulators. This reliable and economical technology eliminates the need for more complex superconducting magnets, except to achieve very high magnetic fields for the production of hard photons from relatively low energy rings. We review the spectral properties of the radiation, emphasizing the complementary aspects of time- and frequency-domain analyses. We next study the brightness of the undulator source. Finally, we consider some limitations associated with operating an undulator in a storage ring.

Description:
The magnetic field pattern in a flat wiggler with iron teeth is discussed. A ''flat'' wiggler is one in which the magnetic fields are all in the vertical direction, alternating in polarity. In the absence of iron, a discussion of such wigglers has been given by J.P. Blewett and R. Chasman. A segment of a flat wiggler is shown. An accurate analytical approximation to the problem for the case when the iron permeability is infinite is presented. Saturation effects in the iron were studied using the POISSON computer program. The analytic approximation in the case of infinite permeability was derived.

Description:
Along the general run of the vacuum chamber synchrotron radiation strikes the wall at a glancing angle of about 5.6/sup 0/. The heat source is well-approximated by a ribbon of uniform power density having a small vertical height and an infinite azimuthal length. The heat transfer problem reduces to one in two-dimensions and it has been considered in a previous note. At the corner of a beam port the angle of incidence becomes 90/sup 0/, so the temperature rises much higher than elsewhere. Since the power density at the corner is not uniform in its azimuthal dependence, but is strongly peaked at the point of normal incidence, two-dimensional heat flow is not a good approximation. The rectangular 3d problem is considered. This is easily solved and yields a good first estimate of the temperature rise at the corner.

Description:
Some heat transfer problems associated with the incidence of synchrotron radiation upon the inner wall of the vacuum chamber are considered. It is assumed that power is supplied to the wall at P watts per azimuthal centimeter, so when the ribbon of radiation has a vertical height d, the incident power per unit area is P/d. Our goal is to determine the maximum temperature to be found on the inner surface of the chamber wall, when the wall has thickness L, and the outer surface of the wall is maintained at temperature T/sub W/ by water cooling. An idealizd two-dimensional potential problem is studied, where the two-dimensional cross-section is taken perpendicular to the electron beam.

Description:
We present an introduction to some fundamental aspects of the theory of free electron lasers. Spontaneous radiation emitted by electrons traversing a wiggler magnet is briefly reviewed, and stimulated emission in the low-gain regime is discussed using Colson's pendulum equations and Madey's theorems. The high-gain regime is treated by an extention of the work of Bonifacio, Pellegrini, and Narducci. We introduce dynamical variables to describe the radiation field, and a Hamiltonian formulation of Maxwell's equations is employed. A canonical transformation to the interaction representation factors out the fast time variation of the radiation field, and the slow time dependence is determined by linearized equations for the appropriate collective variables. As an application of this technique we consider self-amplified spontaneous radiation, and we comment upon the relationship between our approach and the use of coupled Vlasov-Maxwell equations.

Description:
Undulator magnets are used in connection with particle (typically electron) storage rings to enhance the spectrum of synchrotron radiation and are a basic component of free electron lasers. Two configurations are common: helical undulators, for which the magnetic field on the axis is constant in modulus and rotates around the axis as we proceed along it; and transverse undulators, that have a median plane of symmetry. The orientation of the field for a transverse geometry is always the same on the median plane, but the modulus of the field is spatially modulated. For the electron storage rings that constitute the National Synchrotron Light Source at Brookhaven, undulators have been proposed to produce a line spectrum of spontaneous radiation to be used in the experiments. One of these undulators will be used for the free electron laser experiment on the VUV-ring. The basic design of this undulator and its expected performance are discussed.

Description:
A summer study was held in 1977 to provide definitive recommendations on the design of the National Synchrotron Light Source. The group attending the workshop included electron storage ring experts. Topics covered in the proceedings include: introduction to the lattice; partial list of corrective or diagnostic equipment; closed orbit errors in the 2.5 GeV x-ray source; linear horizontal-vertical coupling, vertical dispersion, and control of the vertical closed orbit at the wiggler; bunch lengthening and longitudinal stability; longitudinal stability with a Landau cavity; transverse coupled-bundle instabilities; coupling impedance and power dissipation for a step change in the vacuum chamber; bunch lengthening and widening; aperture limitations by sextupoles; second-order effects of correction sextupoles; horizontal aperture in x-ray ring; introduction of sinusoidal wiggler into the x-ray lattice; the Touchek effect; possible mode of injection into the x-ray ring; and an inquiry into the flexibility of the x-ray lattice. (GHT)

Description:
A dispersion relation is used to study the effect of betatron oscillations on the gain of a guided mode in a free electron laser operating in the high-gain regime before saturation. We assume the electron beam to be matched to the natural focussing of a helical wiggler, and our treatment includes the effects of the finite energy spread and emittance of the electron beam, the transverse gradient in the wiggler, and the variation of the electromagnetic wave transverse phase experienced by the electrons due to betatron oscillations.

Description:
Linearized Vlasov-Maxwell equations are used to derive a partial differential equation determining the 3-dimensional slowly varying envelope function of the radiated electric field. The equation is solved analytically. From the correlation function <E(z,r,t) E*(z',r',t)> of the electric field averaged over the stochastic ansemble describing the initial shot noise in the beam, we compute the longitudinal and transverse correlation lengths sigma/sub L/ and sigma/sub T/. The radiated power S per unit cross-sectional area of the the electron beam is determined. Our analysis is applicable for wiggler length L = N/sub w/lambda/sub w/ long enough for the exponential regime to be researched, but short enough so that L sigma/sub theta/ less than or equal to a, the electron beam radius. 6 refs.

Description:
A circular waveguide is considered whose radius a(z) = a(1+epsilon s(z)) varies periodically with the axial coordinate z. Chatard-Moulin and Papiernik have introduced a perturbation expansion in powers of epsilon for the longitudinal impedance of such a waveguide. The derivation of this expansion is reformulated in a manner which elucidates the structure of the higher-order terms, and allows the determination of the dependence on epsilon of the resonant frequencies. For a square-wave (SW) wall distortion, there are divergent coefficients in the perturbation expansion. Hence, a special treatment is required in this case, and a calculation of the resonant behavior is presented for small epsilon, using an approach which does not assume an expansion in powers of epsilon. The resulting expression for the resonant impedance involves functions singular at epsilon = 0; however, to leading order in epsilon, the loss-factors and resonant frequencies are in agreement with perturbation theory.

Description:
We discuss the relationship of the effective start-up noise in a single pass free electron laser to the spontaneous radiation emitted in the initial gain length of the wiggler magnet. Also, it is noted that the number of modes in the output is related to the phase space volume occupied by the spontaneous radiation emitted in the first gain length. 12 refs.

Description:
We consider the longitudinal instabilities of a bunched beam subject to a non-harmonic rf potential. Assuming the unperturbed bunch to be described by a Maxwell-Boltzmann distribution, our treatment is based upon the linearized Vlasov equation. The formalism developed is exact, and in particular, correctly describes the effect of the dependence on amplitude of the synchrotron oscillation frequency. We discuss the fast blowup limit, and extend Wang and Pellegrini's treatment of the microwave instability to include the case of a non-Gaussian bunch. Next, within the short bunch approximation, we derive the dispersion relation describing the Landau damping of the coupled bunch modes, resulting from the use of a Landau cavity.

Description:
We present an overview of the longitudinal instabilities of Gaussian bunches subject to a harmonic RF potential. Our emphasis is on the behavior of long bunches having lengths greater than the wavelength of the perturbing electromagnetic fields. We exhibit the crossover between the dominance of the synchrotron modes and the coasting-beam-like distortions of the bunch distribution, which occurs as the real or imaginary part of the coherent oscillation frequency becomes large compared to the synchrotron oscillation frequency. For a narrow band impedance the growth rate of the coasting-beam-like modes is determined by the average beam current, and for a broad band impedance the growth rate is determined by the peak current. We discuss the transition between these two regimes by considering the growth rate as a function of the bandwidth of the impedance.

Description:
The group theoretical method of Landau and Lifshitz was used to derive effective Hamiltonians for certain paramagnetic to antiferromagnetic transitions having order-parameters with n greater than or equal to 4 components. A renormalization group analysis in 4-epsilon dimensions was performed. The first- order nature of the order-disorder transitions in Cr(n = 12), Eu(n = 12), UO$sub 2$(n = 6), and MnO(n = 8) can be explained by noting that the corresponding Hamiltonians possess no stable fixed points in 4-epsilon dimensions. It is predicted that all fcc type I(anti m perpendicular anti k), type II and type III(anti m perpendicular [100], anti k = [1/2 01]) antiferromagnetic transitions are first-order. The work is intended to serve as a guide in an experimental search for new examples of first-order transitions. A 2m-component Hamiltonian is also considered which possesses a unique, nonisotropic, stable fixed point for each value of 2m greater than or equal to 4. When 2m = 4, the Hamiltonian describes the paramagnetic to antiferromagnetic transitions in TbAu$sub 2$, DyC$sub 2$, Tb, Ho, Dy, and the structural transition in NbO$sub 2$. If these transitions are second-order, it is predicted they all belong to the same universality class. For 2m = 6, the Hamiltonian describes the antiferromagnetic transitions in TbD$sub 2$, Nd, K$sub 2$IrCl$sub 6$, and MnS$sub 2$. These transitions belong to a single universality class. (auth)

Description:
As the applied magnetic fields are increased during acceleration, eddy currents are induced in the vacuum chamber. These result in magnetic field perturbations which we shall estimate for the Booster and X-Ray Rings. Our calculation follows that of Asner, in particular, we use image currents to satisfy the boundary conditions imposed by the iron poles of the magnets. The strength of the magnetic field perturbations is roughly three times greater with the iron poles present than absent.

Description:
There is a great activity throughout the world in the development of synchrotron radiation facilities to serve as sources for basic and applied research. We discuss some of the the opportunities and challenges presented by the development of ever higher brightness synchrotron radiation sources. 39 refs.

Description:
The advantages of coherent soft x-rays for three-dimensional imaging of biological specimens are discussed, the x-ray source requirements are described, and the general design of the beam line and its optical system are given. (WHK)

Description:
This summary is designed to present to the NSLS user community the possible options for wigglers and undulators. The desire is to make it possible for every user to respond to the request by the NSLS for guidance in insertion device development so that it can best serve their scientific interests. There are many options, each with its own advantages and disadvantages, as well as certain restrictions imposed by the parameters of the NSLS storage rings. The NSLS is asking for input in two areas. First, we must decide on the instrumentation to be developed for the high field superconducting wiggler beam lines and for the hybrid permanent magnet wiggler lines. Secondly, the long-range plans for additional insertion devices are now under discussion. Choices must be made between the large number of different magnets which can be built. To facilitate user response, we provide a review of the properties of wigglers and undulators, introducing the basic concepts and defining the fundamental parameters. A detailed account of the brightness of the undulator source is presented and the insertion devices already under construction for the x-ray and VUV rings are discussed. We describe the suitability of certain proposed undulators for the generation of soft x-rays (5 to 50A), and harder x-rays (3 to 12A).

Description:
There is an active program of accelerator development at the NSLS aimed at improving reliability, stability and brightness. Work is primarily focused on providing improved performance for the NSLS user community, however, important elements of our work have a generic character and should be of value to other synchrotron radiation facilities. In particular, we have successfully operated a small gap undulator with a full vertical beam aperture of only 3.8 mm, with no degradation of beam lifetime. This provides strong support for the belief that small gap, short period devices will play an important role in the future.

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